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Simplifying 5(m + n) + -1(3m + 2n) = 0 (m * 5 + n * 5) + -1(3m + 2n) = 0 (5m + 5n) + -1(3m + 2n) = 0 5m + 5n + (3m * -1 + 2n * -1) = 0 5m + 5n + (-3m + -2n) = 0 Reorder the terms: 5m + -3m + 5n + -2n = 0 Combine like terms: 5m + -3m = 2m 2m + 5n + -2n = 0 Combine like terms: 5n + -2n = 3n 2m + 3n = 0 Solving 2m + 3n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3n' to each side of the equation. 2m + 3n + -3n = 0 + -3n Combine like terms: 3n + -3n = 0 2m + 0 = 0 + -3n 2m = 0 + -3n Remove the zero: 2m = -3n Divide each side by '2'. m = -1.5n Simplifying m = -1.5n
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